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HESI A2 Mathematics practice questions

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These are original practice items written to the HESI A2 blueprint (4 options, no penalty for wrong answers), not actual exam questions. Try each one before you open the answer.

Practice by topic

Topics come from the tags on our own items, so this list reflects what the bank actually covers in Mathematics rather than a generic syllabus.

Mathematics: Fractions 71 in the bank Mathematics: Unit and Dosage Conversions 49 in the bank Mathematics: Ratios and Proportions 44 in the bank Mathematics 38 in the bank Mathematics: Basic Algebra 38 in the bank Mathematics: Percentages 33 in the bank Mathematics: fractions and decimals 33 in the bank

Mathematics sample questions

Question 1

A nurse needs to administer a medication that requires mixing 1/3 cup of solution A with 1/4 cup of solution B. What is the total volume of the mixture in cups?

  1. A 1/12
  2. B 5/7
  3. C 2/7
  4. D 7/12
Show the answer and explanation

Correct answer: D

To add fractions with different denominators, find a common denominator. The least common denominator of 3 and 4 is 12. Convert: 1/3 = 4/12, 1/4 = 3/12. Sum = 7/12 cup.

Why the other options are wrong:
A: 1/12 comes from subtracting instead of adding (4/12 - 3/12).
B: 5/7 results from adding numerators (1+1=2) and denominators (3+4=7) and then incorrectly simplifying? Actually 2/7 is already that; 5/7 might come from adding 1/3+1/4 as 0.333+0.25=0.583, then rounding? No clear error pattern.
C: 2/7 results from incorrectly adding numerators and denominators (1+1=2, 3+4=7).

Question 2

A patient's temperature dropped from 102°F to 97.5°F. What is the percent decrease? (Round to the nearest tenth of a percent.)

  1. A 4.6%
  2. B 5.0%
  3. C 4.5%
  4. D 4.4%
Show the answer and explanation

Correct answer: D

Decrease = 102 - 97.5 = 4.5°F. Percent decrease = (4.5 / 102) × 100 ≈ 4.4118%, which rounds to 4.4%.

Why the other options are wrong:
A: 4.6% might come from rounding 4.4118% up incorrectly or using 4.5/97.5 ≈ 4.6%.
B: 5.0% might come from using 5 as the decrease (102 - 97 = 5) or dividing by 100 instead of 102.
C: 4.5% would result from using the decrease as the percentage without dividing by the original (4.5/100 = 4.5%).

Question 3

Express the fraction 3/4 as a decimal.

  1. A 0.25
  2. B 0.75
  3. C 0.34
  4. D 0.50
Show the answer and explanation

Correct answer: B

Divide the numerator by the denominator: 3 ÷ 4 = 0.75.

Why the other options are wrong:
A: 0.25 equals 1/4; it may come from computing 1 - 3/4 instead of 3/4.
C: 0.34 simply writes the digits 3 and 4 after a decimal point instead of dividing 3 by 4.
D: 0.50 equals 1/2 (or 2/4), which is less than 3/4.

Question 4

A patient's hematocrit is 42%. The normal range is 37% to 47%. What percentage of the normal range does this value represent? (Assume the normal range is a continuous interval.)

  1. A 50%
  2. B 89%
  3. C 42%
  4. D 60%
Show the answer and explanation

Correct answer: A

The normal range spans 10 percentage points (47 – 37 = 10). The patient's value of 42% is 5 points above the lower bound (42 – 37 = 5). So it is 5/10 = 50% of the range.

Why the other options are wrong:
B: 89% is approximately 42/47, which compares the value to the upper bound, not the range.
C: 42% is the patient's hematocrit value, not the percentage of the range.
D: 60% might come from 42/37? No, that is over 100%. Possibly a miscalculation.

Question 5

A clinic's monthly budget of 60,000 dollars allocates 40 percent to staffing and 25 percent to supplies, with the remainder going to overhead. How much money is allocated to overhead each month?

  1. A $24,000
  2. B $21,000
  3. C $39,000
  4. D $15,000
Show the answer and explanation

Correct answer: B

Overhead receives the remainder: 100% - 40% - 25% = 35%. Then 0.35 × 60,000 = 21,000 dollars.

Why the other options are wrong:
A: $24,000 is the staffing share (40% of 60,000), not overhead.
C: $39,000 is staffing plus supplies (65%), not the remaining 35%.
D: $15,000 is the supplies share (25% of 60,000), not overhead.

Question 6

A medication label states that 2 tablets contain 1.5 mg of active ingredient. How many tablets are needed to administer 2.5 mg?

  1. A 4
  2. B 5
  3. C 3 1/3
  4. D 3
Show the answer and explanation

Correct answer: C

Set up proportion: 2 tablets / 1.5 mg = x tablets / 2.5 mg. Cross multiply: 1.5x = 5, so x = 5/1.5 = 10/3 = 3 1/3 tablets.

Why the other options are wrong:
A: 4 tablets would give 3.0 mg, too much.
B: 5 tablets would give 3.75 mg, too much.
D: 3 tablets would give only 1.5 × 1.5 = 2.25 mg, insufficient.

Question 7

A nurse must administer a drug at 0.5 mg per kg of body weight. The patient weighs 176 lb. The available vial contains 50 mg of drug in 2 mL. How many mL should the nurse administer?

  1. A 3.2
  2. B 0.8
  3. C 1.6
  4. D 4.0
Show the answer and explanation

Correct answer: C

Convert weight: 176 lb ÷ 2.2 = 80 kg. Dose = 0.5 mg/kg × 80 kg = 40 mg. Concentration = 50 mg / 2 mL = 25 mg/mL. Volume = 40 mg ÷ 25 mg/mL = 1.6 mL.

Why the other options are wrong:
A: 3.2 mL would result if the dose were calculated as 0.5 mg/kg × 80 kg = 40 mg, then dividing by 12.5 mg/mL (misreading concentration).
B: 0.8 mL might come from dividing 40 mg by 50 mg/mL, forgetting the volume of the vial.
D: 4.0 mL could be obtained by using 80 kg × 0.5 mg/kg = 40 mg and then dividing by 10 mg/mL, an incorrect concentration.

Question 8

Convert 0.75 liters to milliliters.

  1. A 7500 mL
  2. B 750 mL
  3. C 75 mL
  4. D 7.5 mL
Show the answer and explanation

Correct answer: B

1 L = 1000 mL, so 0.75 × 1000 = 750 mL.

Why the other options are wrong:
A: 7500 mL is off by a factor of 10 (7.5 L).
C: 75 mL is off by a factor of 10 (0.075 L).
D: 7.5 mL is off by a factor of 100 (0.0075 L).

Question 9

Solve for x: 2(x + 3) - 4 = 3x + 1.

  1. A 0
  2. B 1
  3. C -1
  4. D 2
Show the answer and explanation

Correct answer: B

Distribute: 2x + 6 - 4 = 3x + 1 → 2x + 2 = 3x + 1. Subtract 2x from both sides: 2 = x + 1. Subtract 1: x = 1.

Why the other options are wrong:
A: 0 might come from forgetting to distribute the 2 or incorrectly moving terms.
C: -1 would result from an error in combining like terms or sign mistakes.
D: 2 might come from adding instead of subtracting after isolating x.

Question 10

A disinfectant solution requires a ratio of 5 parts alcohol to 3 parts water. If a nurse needs to prepare 480 mL of this solution, how many milliliters of alcohol are needed?

  1. A 300 mL
  2. B 320 mL
  3. C 240 mL
  4. D 180 mL
Show the answer and explanation

Correct answer: A

A 5:3 ratio has 8 parts. Each part is 480 mL ÷ 8 = 60 mL, so the alcohol is 5 × 60 = 300 mL and the water is 180 mL.

Why the other options are wrong:
B: 320 mL takes two thirds of 480, which does not match a 5:3 ratio.
C: 240 mL splits the total in half, treating the ratio as 1:1.
D: 180 mL is the water portion (3 parts), not the alcohol.

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